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Question Number 15192 by arnabpapu550@gmail.com last updated on 08/Jun/17

$$\mathrm{Let}{D}_r=\left|\begin{array}{ccc}{2}^{r-1}& 2\cdot 3^{r-1}& 4\cdot 5^{r-1}\\ \alpha & \beta & \gamma \\ 2^n-1& 3^n-1& 5^n-1\end{array}\right|.$$$$\mathrm{Then}\mathrm{the}\mathrm{value}\mathrm{of}\underset{r=1}{\sum ^n}{D}_r\mathrm{is}$$

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